Clipping distortion canceller for OFDM signals

ABSTRACT

Methods and apparatus are provided for reducing clipping noise from an OFDM signal, the methods and apparatus are operable to carry out actions including: (a) transforming a received orthogonal frequency division multiplexed (OFDM) signal from a transmission channel into the frequency domain, the OFDM signal having been subject to a clipping function prior to transmission in order to reduce the peak-to-average power ratio (PAPR); (b) recovering data symbols from the transformed OFDM signal, which include clipping noise; (c) estimating the clipping noise in the frequency domain based on the data symbols; and (d) subtracting the estimated clipping noise from the transformed OFDM signal.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application is a Continuation of U.S. patent applicationSer. No. 10/771,249, filed on Feb. 3, 2004, now U.S. Pat. No. 7,031,251,titled “Clipping Distortion Canceller for OFDM Signals,” by Chen,assigned to the assignee of the presently claimed subject matter.

This application claims the benefit of U.S. Provisional PatentApplication No.: 60/446,708, entitled CLIPPING DISTORTION CANCELLER FOROFDM SIGNALS, filed Feb. 12, 2003, the entire disclosure of which ishereby incorporated by reference.

BACKGROUND

Orthogonal frequency division multiplexing (OFDM) is one of thetechnologies considered for 4G broadband wireless communications due toits robustness against multipath fading and relatively simpleimplementation compared to single carrier systems. To preserve bothamplitude and phase information, OFDM transmitters utilize linear poweramplifiers. One of the main drawbacks of using OFDM is the high cost oflinear power amplifiers with high dynamic range. Such amplifiers areused because the OFDM signals have a high peak-to-average power ratio(PAPR), particularly since the OFDM signal will usually consists of alarge number of subcarriers.

Various techniques have been proposed to reduce the PAPR of OFDMsignals. For example the following publications describe some of thesetechniques: J. Davis and J. Jedwab, “Peak-to-mean power control in OFDM,Golay Complementary Sequences, and Reed-Muller Codes,” IEEE Transactionson Information Theory, Vol. 45, pp. 2397-2417 (November 1999); A. D. S.Jayalath and C. Tellambura, “Reducing the Peak-to-Average Power Ratio ofan OFDM Signal Through Bit or Symbol Interleaving,” IEEE ElectronicsLetters, Vol. 36, pp. 1161-1163 (June 2000); and H. Ochiai and H. Imai,“Performance Analysis of Deliberately Clipped OFDM Signals,” IEEETransactions on Communications, Vol. 50, pp. 89-101 (January 2002), theentire disclosures of each of these publications are incorporated hereinby reference.

With respect to the latter approach, the deliberate clipping of the OFDMsignal before amplification is a simple and efficient way of controllingthe PAPR. The clipping process is characterized by the clipping ratio(CR), defined as the ratio between the clipping threshold and the RMSlevel of the OFDM signal. Clipping is a non-linear process, which maylead to significant distortion and performance loss. In particular,clipping at the Nyquist sampling rate will cause all the clipping noiseto fall in-band and suffers considerable peak re-growth after digital toanalog (D/A) conversion.

In the H. Ochiai and H. Imai paper and in X. Li and L. J. Cimini,“Effects of Clipping and Filtering on the Performance of OFDM,” in Proc.IEEE Vehicular Technology Conf. (VTC), pp. 1634-1638 (May 1997) (theentire disclosure of which is hereby incorporated by reference), it wasshown that clipping an over-sampled OFDM signal reduces the peakre-growth after D/A conversion and generates less in-band distortion.But this technique causes out-of-band noise that needs to be filtered.

The problem of distortion caused by intentional clipping and theattendant out-of-band noise is a significant issue in connection withusing OFDM, particularly since clipping noise is the significant factorlimiting performance in OFDM systems operating at high signal to noiseratio (SNR).

Although techniques have been proposed for mitigating the effect ofclipping noise, they are less than satisfactory. The followingpublication illustrate this point: D. Kim and G. L. Stuber, “ClippingNoise Mitigation for OFDM by Decision-aided Reconstruction,” IEEECommunications Letters, Vol. 3, pp. 4-6 (January 1999); and H. Saedi, M.Sharif, and F. Marvasti, “Clipping Noise Cancellation in OFDM SystemsUsing Oversampled Signal Reconstruction,” IEEE Communications Letters,Vol. 6, pp. 73-75 (February 2002). In both cases, however, acceptableloss in SNR (e.g., about less than 1 dB) is achieved only for CR≧4 dB.Furthermore, the decision-aided reconstruction approach described in theD. Kim and G. L. Stuber publication only applies to Nyquist rateclipping. Finally, the use of over-sampled signal reconstructiondisclosed in the H. Saedi, M. Sharif, and F. Marvasti publication alsorequires significant bandwidth expansion to work well.

A fundamental characteristic of these approaches, as well as otherproposed methods, is that they attempt to reconstruct the affected (orlost) time domain signal samples resulting from clipping. It is believedthat the reconstruction of time domain signals is inherently error proneand, thus, undesirable.

Accordingly, there are needs in the art for new methods and apparatusfor processing OFDM signals in order to at least one of reduce PAPR,reduce distortion and out of band radiation.

SUMMARY OF THE INVENTION

While the present invention is not limited by any theory of operation,various aspects of the present invention exploit the fact that, unlikeall white Gaussian noise (AWGN), clipping noise is generated by a knownprocess, which can be recreated at the receiver and subsequentlyremoved. Based on this observation and the analysis of the clippingprocess, a novel iterative clipping noise cancellation is achievable forclipped and filtered OFDM signals in accordance with one or more aspectsof the present invention.

The various aspects of the clipping noise cancellation approachdiscussed and claimed herein are applicable to any of the deliberateclipping approaches and any of the repeated clipping approaches (whichis an extension of deliberate clipping).

In accordance with one or more aspects of the present invention, amethod includes: (a) transforming a received orthogonal frequencydivision multiplexed (OFDM) signal from a transmission channel into thefrequency domain, the OFDM signal having been subject to a clippingfunction prior to transmission in order to reduce the peak-to-averagepower ratio (PAPR); (b) recovering data symbols from the transformedOFDM signal, which include clipping noise; (c) estimating the clippingnoise in the frequency domain based on the data symbols; and (d)subtracting the estimated clipping noise from the transformed OFDMsignal.

In accordance with one or more further aspects of the present invention,an apparatus includes: a receiver operable to receive an orthogonalfrequency division multiplexed (OFDM) signal from a transmissionchannel, the OFDM signal having been subject to a clipping functionprior to transmission in order to reduce the peak-to-average power ratio(PAPR); a frequency transform unit operable to transform the OFDM signalto the frequency domain; a decoding unit operable to recover datasymbols from the frequency domain OFDM signal, which include clippingnoise; a noise estimator operable to estimate the clipping noise in thefrequency domain based on the data symbols; and a difference circuitoperable to subtract the estimated clipping noise from the transformedOFDM signal.

In accordance with one or more further aspects of the present invention,an apparatus includes a processor operating under the control of one ormore software programs that cause the processor to carry out actions,including: (a) transforming a received orthogonal frequency divisionmultiplexed (OFDM) signal from a transmission channel into the frequencydomain, the OFDM signal having been subject to a clipping function priorto transmission in order to reduce the peak-to-average power ratio(PAPR); (b) recovering data symbols from the transformed OFDM signal,which include clipping noise; (c) estimating the clipping noise in thefrequency domain based on the data symbols; and (d) subtracting theestimated clipping noise from the transformed OFDM signal.

In accordance with one or more further aspects of the present invention,a storage medium contains one or more software programs that areoperable to cause a processor executing the one or more softwareprograms to carry out actions, including: (a) transforming a receivedorthogonal frequency division multiplexed (OFDM) signal from atransmission channel into the frequency domain, the OFDM signal havingbeen subject to a clipping function prior to transmission in order toreduce the peak-to-average power ratio (PAPR); (b) recovering datasymbols from the transformed OFDM signal, which include clipping noise;(c) estimating the clipping noise in the frequency domain based on thedata symbols; and (d) subtracting the estimated clipping noise from thetransformed OFDM signal.

In accordance with one or more further aspects of the present invention,the methods and apparatus for controlling cache memories described thusfar and/or described later in this document, may be achieved utilizingsuitable hardware, such as that shown in the drawings hereinbelow. Suchhardware may be implemented utilizing any of the known technologies,such as standard digital circuitry, analog circuitry, any of the knownprocessors that are operable to execute software and/or firmwareprograms, one or more programmable digital devices or systems, such asprogrammable read only memories (PROMs), programmable array logicdevices (PALs), any combination of the above, etc.

Further, the methods of the present invention may be embodied in asoftware program that may be stored on any of the known or hereinafterdeveloped media.

Other aspects, features and advantages of the present invention willbecome apparent to those skilled in the art when the description hereinis taken in conjunction with the accompanying drawing.

BRIEF DESCRIPTION OF THE DRAWING

For the purposes of illustration, there are forms shown in the drawingsthat are presently preferred, it being understood, however, that theinvention is not limited to the precise arrangements andinstrumentalities shown.

FIG. 1 is a block diagram illustrating a transmitter and a receiverincorporating a distortion cancellation feature in accordance with oneor more aspects of the present invention;

FIGS. 2 a-2 b are block diagrams illustrating a preferred approach toachieving a deliberately clipped OFDM signal, which may be employed inthe transmitter and/or the receiver of FIG. 1 in accordance with one ormore aspects of the present invention;

FIG. 3 is a graphical illustration of test results indicating thecomplementary cumulative density function (CCDF) versus the PAPR of adigitally clipped OFDM signal (with a clipping ratio of 1) in accordancewith one or more aspects of the present invention;

FIG. 4 is a graphical illustration of test results indicating the packeterror rate (PER) versus (E_(b)/N₀) of the receiver of FIG. 1 over anAWGN channel including comparisons with the “signal reconstruction”approach;

FIG. 5 is a graphical illustration of test results indicating the packeterror rate (PER) versus (E_(b)/N₀) of the receiver of FIG. 1 (employingdeliberate clipping) over a Rayleigh fading channel includingcomparisons with the “signal reconstruction” approach;

FIG. 6 is a block diagram illustrating a preferred approach to achievinga repeatedly clipped OFDM signal, which may be employed in thetransmitter and/or the receiver of FIG. 1 in accordance with one or moreaspects of the present invention;

FIG. 7 is a graphical illustration of test results indicating thecomplementary cumulative density function (CCDF) versus the PAPR of arepeatedly clipped OFDM signal (with a clipping ratios of 1.5, 1.3, and1.35) in accordance with one or more aspects of the present invention;and

FIG. 8 is a graphical illustration of test results indicating the packeterror rate (PER) versus (E_(b)/N₀) of the receiver of FIG. 1 (employingrepeated clipping) over a Rayleigh fading channel including comparisonswith the “signal reconstruction” approach.

DETAILED DESCRIPTION OF THE INVENTION

In general, the present invention is directed to methods and apparatusfor iteratively estimate and cancel the distortion caused by clippingnoise at the receiver. experimentation and simulation has shown that themethods and apparatus of the present invention may be applied to clippedand filtered OFDM signals such that (for an IEEE 802.11a system) thePAPR can be reduced to as low as 4 dB while the system performance canbe restored to within 1 dB of the non-clipped case with only moderatecomplexity increase and with substantially no bandwidth expansion.

In this regard, reference is now made to FIG. 1, which is a blockdiagram of a system 100 including a transmitter 102 and a receiver 104incorporating one or more distortion cancellation features in accordancewith one or more aspects of the present invention. It is understood thatthe system 100 is disclosed by way of block diagram to illustrate alogical partitioning of functional blocks, which may be considered ashardware elements, software routines, digital signal processing (DSP)routines, and/or straight method elements. It is also noted that thefunctional partitioning is provided by way of example only, it beingunderstood that many variations of partitioning are contemplated withoutdeparting from the spirit and scope of the present invention.

The transmitter 102 preferably includes an encoder 106, aninterleaving/mapping element 108, a clipping element 110, an inversefrequency domain transform element 112 (such as an inverse fast Fouriertransform, IFFT), and an output stage 114 (which may include among otherthings an antenna). It is understood that the apparatus and/or processelements needed to achieve signal transmission over the air (or othertransmission channel) preferably adhere to the requirements of the802.11a standard (or protocol), e.g., with respect to operationalfrequency parameters, sub-carrier frequency parameters, powerrequirements, coding parameters, symbol definitions, bit rates, otherprotocol parameters, etc., which are all well known in the art.

The encoder 106 is operable to improve system performance (e.g., lowerthe error rate) by adding information data (redundancy) to the inputdata bits. For example, if the input data bits into the encoder 106 aregrouped segments of two bits long (e.g., 00, 01, 10, 11), the encodermay output encoded data bits (or coded data bits) of four bits in length(e.g., 1011, etc.). This has an advantageous effect at the receiver(which as will be discussed below includes a corresponding decoder 136).The decoder 136 takes the received data signals for the four bits (e.g.,1011), which will be influenced by noise, and make a decision as to whattwo information bits correspond to the received four bits (plus noise).If the signal to noise ratio (SNR) is high enough, the decoder willoutput the proper two bits (e.g., 00). If the SNR is low, the decodermay output the wrong symbol in error. Any of the known (or hereinafterdeveloped) encoders may be employed in connection with the presentinvention.

The interleaving/mapping element 108 may be two separate functionalelements, one for interleaving and one for mapping, although forsimplicity they are illustrated in integral fashion. As for theinterleaving function, the coded data bits are interleaved (permutated)before being mapped to symbols. The major purpose for using interleavingis to combat the affects of multi-path fading channels. Any of the known(or hereinafter developed) interleaving techniques may be employedwithout departing from the spirit and scope of the present invention.For example, an IEEE standard 802.11a block interleaver may be suitablefor used in connection with implementing the present invention. The802.11a interleaver is defined by a two-step permutation. The firstpermutation ensures that adjacent coded bits are mapped onto nonadjacentsub-carriers. The second permutation ensures that adjacent coded bitsare mapped alternately onto less and more significant bits of theconstellation and, thereby, long runs of low reliability (LSB) bits areavoided.

The interleaved data bits are then mapped into multi-level phasesignals. For example, the mapping may be in accordance with the M-QAMtechnique (quadrature amplitude modulation), such as 16-QAM, where bits0000 are mapped to a complex signal point −3−3i; bits 1001 are mapped to−1+3i, etc. Alternatively, the mapping may be in accordance with theM-PSK technique (phase shift keying). Those skilled in the art willappreciate that there are other known mapping techniques, which forsimplicity are not discussed in detail but are inherently within thepurview of the present invention. The output of the mapping function aremodulated symbols.

The clipping element 110 is operable to limit the PAPR of the OFDMsignal before amplification and transmission. Preferably the clippingfunction is performed digitally. To reduce peak power re-growth anddistortion, the time domain signal is preferably over-sampled by afactor greater than two and then the amplitude of the time domain signalsamples are limited by a threshold A (i.e., they are clipped). Furtherdetails regarding the clipping element 110 will be discussed below.

Following clipping, each modulated signal is assigned to a sub-carriervia the IFFT element 112 and transmitted over the transmission channel(such as air).

In connection with the foregoing, a low-pass equivalent of an OFDMsignal can be represented by the following equation:

$\begin{matrix}{{{s(t)} = {{\frac{1}{\sqrt{N}}{\sum\limits_{k = 0}^{N - 1}{C_{k}{\exp( {{j2\pi}\;{kf}_{0}t} )}\mspace{14mu} 0}}} \leq t \leq T}},} & (1)\end{matrix}$

where N is the number of sub-carriers, f₀ is the sub-carrier spacing, Tis the symbol duration, C_(k) is the complex modulated symbol. Inkeeping with the IEEE standard 802.11a, the modulated symbols areobtained by mapping an encoded bit stream. An OFDM block consists of thesequence of symbols {C_(k)}_(k=0) ^(N−1).

The PAPR of the transmitted OFDM signal may be defined by the followingequation:

$\begin{matrix}{{{PAPR} = \frac{\max_{0 \leq t \leq T}{{s(t)}}^{2}}{P_{av}}},} & (2)\end{matrix}$where P_(av) is the average power of the transmitted symbol and themaximum is sought over the symbol duration. Note that the PAPR ofequation (2) is defined for the average power P_(av) measured afterclipping and filtering.

Although any of the known (or hereinafter developed) clipping techniquesmay be employed in connection with the present invention, it ispreferred that a deliberate clipping approach as illustrated in FIGS. 2a-2 b is used. It is noted that FIG. 2 a illustrates a soft envelopelimiter for an OFDM signal, while FIG. 2 b illustrates further detailsof the band pass filter (BPF) of FIG. 2 a. For simplicity, the detailsof FIGS. 2 a-2 b will not be described in detail herein as it isunderstood that one skilled in the art would know how to implement theclipping element illustrated. Further details concerning the clippingtechnique illustrated in FIGS. 2 a-2 b may be found in H. Ochiai and H.Imai, “Performance Analysis of Deliberately Clipped OFDM Signals,” IEEETransactions on Communications, Vol. 50, pp. 89-101 (January 2002), theentire disclosure of which is hereby incorporated by reference.

Referring again to the clipping element 110 of FIG. 1, such elementincludes an IFFT circuit 116, a clipping circuit 118, an FFT circuit 120and an out of band removal circuit 122. In this regard, the IFFT circuitmay operate to sample the OFDM signal of equation (1) at time intervalsof Δt=T/JN, where J is the over-sampling factor. To reduce peak powerregrowth and distortion, the time domain signal may be over-sampled by afactor greater than two. An over-sampled signal can be obtained bypadding {C_(k)}_(k=0) ^(N−1) with (J−1)*N zeros and taking the inversediscrete Fourier transform (IDFT), or the inverse fast Fourier transform(IFFT). The discrete-time OFDM signal sampled at time instant t=nΔt maythen be expressed by the following equation:s _(n) @s(nΔt) n=0, . . . , JN−1.  (3)

The clipping circuit 118 operates to limit the amplitude of the timedomain signal samples via a threshold A. In this regard, let s _(n) be aclipped time sample with the phase left unchanged. Then,

$\begin{matrix}{{{\overset{\_}{s}}_{n}} = \{ \begin{matrix}{s_{n}} & {{{{if}\mspace{14mu}{s_{n}}} \leq A}\;} \\A & {{{{if}{\mspace{14mu}\;}{s_{n}}} > {A.}}\mspace{11mu}}\end{matrix} } & (4)\end{matrix}$

The clipped signal { s _(n)}_(n=0) ^(JN−1) can be modeled as theaggregate of an attenuated signal component and clipping noise{d_(n)}_(n=0) ^(JN−1)s _(n) =αs _(n) +d _(n) n=0, . . . , JN−1  (5)where the attenuation factor α is a function of the clipping ratio γ,defined as γ=A/√{square root over (P_(in))}, with P_(in) the averagesignal power before clipping:

$\begin{matrix}{\alpha = {1 - {\mathbb{e}}^{- \gamma^{2}} + {\frac{\sqrt{\pi}\gamma}{2}{{{erfc}(\gamma)}.}}}} & (6)\end{matrix}$

The FFT circuit 120 and the out of band removal circuit 122 operate toremove the out-of-band components resulting from clipping. The timedomain samples of equation (5) are converted back to frequency domainvia the FFT circuit 120 by applying the discrete Fourier transform (DFT)or the fast Fourier transform to the sequence { s _(n)}_(n=0) ^(JN−1),to obtain the sequence { C _(k)}_(k=0) ^(JN−1). Using equation (5), theterms C _(k) can be expressed by the following:C _(k) =αC _(k) +D _(k) k=0, . . . , JN−1,  (7)where {C_(k)}_(k=0) ^(JN−1) and {D_(k)}_(k=0) ^(JN−1) are respectively,the DFT of {s_(n)}_(n=0) ^(JN−1) and {d_(n)}_(n=0) ^(JN−1) in equation(5). In particular, {D_(k)}_(k=0) ^(JN−1) is the sequence representingthe clipping noise in the frequency domain. The out of band removalcircuit operates to remove the out-of-band components by processing onlythe in-band-components { C _(k)}_(k=0) ^(N−1) through the IFFT circuit112 (which may be an N-point IDFT).

The resulting sequence is transmitted over the antenna 114.

In accordance with one or more aspects of the present invention, theclipping process is repeated at the receiver 104 using the detectedsymbols. Thereafter, the frequency domain clipping noise is estimatedand canceled. The receiver 104 operates in an iterative fashion toachieve this result. The receiver 104 preferably includes an antenna130, an FFT circuit 132, a de-mapping and de-interleaving circuit 134, adecoder 136, an interleaving and mapping circuit 138, a clipping element140, an attenuation circuit 142, an adder 144, an H circuit 154, andanother adder 156.

The FFT circuit 132 operates to convert the signals received from theantenna 130 into the frequency domain (for example using the discreteFourier transform). The adder 156 operates to subtract an estimate ofthe clipping noise from the output of the FFT circuit 132 (which will bediscussed later herein). Assuming perfect synchronization and followingDFT, the signal at the receiver may be expressed as follows:Y _(k) =H _(k)(αC _(k) +D _(k))+Z _(k) k=0, . . . ,N−1,  (8)where H_(k) is the complex channel gain of the k-th sub-carrier assumedto be perfectly known and Z_(k) is AWGN.

Basically, the de-mapping and de-interleaving circuit 134 and thedecoder circuit 136 operate to decode and detect the channelobservations {Y_(k)}_(k=0) ^(N−1).

The de-mapping and de-interleaving circuit 134 performs two basicfunctions. First, the received signal over each sub-carrier isdemodulated (de-mapped) into signals of several bits (i.e., the reverseof the modulation/mapping process performed in the transmitter 102).This sequence of demodulated signals is then de-interleaved (i.e., thereverse of the interleaving process performed in the transmitter 102).This results in the original order prior to the interleaving processcarried out in the transmitter 102.

Next the signals are passed to the decoder circuit 136 to be decoded.Although any of the known decoders may be employed without departingfrom the spirit and scope of the invention, it is preferred that thedecoder is complementary to the encoder 106 of the transmitter 102,which both adhere to the IEEE 802.11a standard. Using the examplepresented above with respect to the encoder 106 of the transmitter 102,the decoder 136 takes the received data signals for the four bits (e.g.,1011), which will be influenced by noise, and make a decision as to whattwo information bits correspond to the received four bits (plus noise).If the signal to noise ratio (SNR) is high enough, the decoder willoutput the proper two bits (e.g., 00). If the SNR is low, the decodermay output the wrong symbol in error.

The decisions of the transmitted sequence obtained by the decoder 136may be denoted as {Ĉ_(k)}_(k=0) ^(N−1). This sequence {Ĉ_(k)}_(k=0)^(N−1) is processed through the interleaving and mapping circuit 138,which may be (and preferably is) of substantially the same functionalityas the interleaving and mapping element 108 of the transmitter 102. Theresultant signal is then subject to two branches. One branch regeneratesthe attenuated frequency domain samples of the non-clipped signals{αĈ_(k)}_(k=0) ^(N−1). This is achieved by passing the signal from theinterleaving and mapping circuit 138 through the attenuation circuit142.

The other branch regenerates the clipped signals at the receiver bypassing the {Ĉ_(k)}_(k=0) ^(N−1) through the clipping element 140.Preferably the clipping element 140 is substantially similar to theclipping element 110 of the transmitter 102. Thus, the clipping element140 preferably includes an IFFT circuit 146, a clipping circuit 148, anFFT circuit 150 and an out of band removal circuit 152, which operate asdiscussed above with respect to the transmitter 102. In this regard, onemay denote the regenerated clipped samples as {G_(k)}_(k=0) ^(N−1). In asubstantially similar was as discussed above with respect to equation(7), the clipped signals can be represented as the sum of an attenuatednon-clipped signal αĈ_(k) and the clipping noise {circumflex over(D)}_(k), as follows:G _(k) =αĈ _(k) +{circumflex over (D)} _(k) k=0, . . . , N−1.  (9)

Since G_(k) and Ĉ_(k) are observable and α can be computed from equation(6), the clipping noise {circumflex over (D)}_(k) can be estimated asfollows:{circumflex over (D)}_(k) =G _(k) −αĈ _(k) k=0, . . . , N−1.  (10)

The summing circuit 144 is operable to subtract the estimated clippingnoise terms {circumflex over (D)}_(k) from the current channelobservation to obtain a refined channel observation for the nextiteration, as follows:

$\begin{matrix}{{{\hat{Y}}_{k} = {Y_{k} - {H_{k}{\hat{D}}_{k}}}}\begin{matrix}{{k = 0},\ldots\mspace{14mu},{N - 1}} \\{{= {{\alpha\; H_{k}C_{k}} + {H_{k}( {D_{k} - {\hat{D}}_{k}} )} + Z_{k}}},}\end{matrix}} & (11)\end{matrix}$where (D_(k)−{circumflex over (D)}_(k)) is the residual clipping noiseand H is the transfer function of block 154. This block 154 multipliesthe input signals {{circumflex over (D)}_(k)}_(k=0) ^(N−1), theestimated clipping noise over each sub-carrier, with the complex channelgains {H_(k)}_(k=0) ^(N−1), where N is the number of sub-carriers.

This process is repeated iteratively, where {Y_(k)}_(k=0) ^(N−1) isreplaced with {Ŷ_(k)}_(k=0) ^(N−1). As the iterations proceed, theestimation of the clipping noise components {{circumflex over(D)}_(k)}_(k=0) ^(N−1) becomes more and more accurate and the receiverperformance is improved.

The above discussion of FIG. 1 reveals that each iteration for clippingnoise estimation and cancellation requires a single pair of IFFT/FFToperations and decoding. Experimentation has shown that only about twosuch iterations are required to achieve satisfactory cancellation, whichimplies that the proposed method and apparatus of the invention requiresonly a moderate increase of complexity at the receiver 104.

While the methods and apparatus of the present invention estimate andcancel the clipping noise, prior art alternative signal reconstructionapproaches attempt to restore the clipped signal to its non-clippedform. These prior art techniques are more sensitive to decision errors.Indeed, using the notation developed and discussed above, the estimateddifference between the frequency domain samples of the non-clipped andclipped signals may be defined as follows: ΔC_(k)=Ĉ_(k)−G_(k). Then, thereconstructed frequency domain samples may be expressed as follows:Ŷ _(k) ^((R)) =Y _(k) +H _(k) ΔC _(k) k=0, . . . , N−1.  (12)

Substituting ΔC_(k)=Ĉ_(k)−G_(k) and G_(k) from equation (9), andapplying the first relation in equation (11), the following results:

$\begin{matrix}{\begin{matrix}{{\hat{Y}}_{k}^{(R)} = {Y_{k} - {H_{k}{\hat{D}}_{k}} + {( {1 - \alpha} )H_{k}{\hat{C}}_{k}}}} \\{= {{\hat{Y}}_{k} + {( {1 - \alpha} )H_{k}{\hat{C}}_{k}}}}\end{matrix}{{k = 0},\ldots\mspace{14mu},{N - 1.}}} & (13)\end{matrix}$

This evidences the differences between various aspects of the presentinvention and the prior art techniques. Indeed, Ŷ_(k) ^((R)), thereconstructed observation with the signal restored to its non-clippedform, has an extra term (1−α)H_(k)Ĉ_(k) compared to Ŷ_(k), the correctedobservation with the clipping noise removed. Note that Ĉ_(k) is thedecision at the previous iteration and should not be directly passed tothe next iteration as part of the refined channel observation. Hence,equation (12) contains an additional term, which will propagate decisionerrors. Only for large clipping ratios α≈1, is this error termnegligible.

Simulations have been conducted using the methods and apparatusdescribed above with respect to FIG. 1. These simulations have beenconducted for clipped and filtered OFDM signals over both AWGN andfading channels. The clipping approach used in the simulations was thatillustrated in FIG. 2 with a clipping ratio set to γ=1 and theout-of-band radiation removed. The simulation model was designed tomatch IEEE Std. 802.11a. The convolutional encoders used in thesimulation were the industry standard constraint length 7, rate ½ withgenerator polynomials g₀=133₈ and g₁=171₈. The number of sub-carrierswas N=64, and the modulation was 16-QAM. Decoding was carried out usinga soft Viterbi algorithm. The system performance is measured based onthe packet error rate (PER), where each packet consists of 16 OFDMsymbols. The E_(b)/N₀ is measured after signal clipping and filtering.

With reference to FIG. 3, the complementary cumulative density function(CCDF) of the PAPR of digitally clipped OFDM signals with out-of-bandradiation removed is illustrated. For a clipping ratio of γ=1, the PAPRis reduced from 12 dB to 6 dB.

With reference to FIG. 4, the simulated packet error rate (PER)performance of the receiver 104 over the AWGN channel is illustrated.The performance is compared with that of a receiver without clippingnoise cancellation and to a receiver with signal reconstruction. Forreference, the performance of a system without clipping is alsoprovided. For the methods and apparatus of the present invention, a gainof about 2 dB relative to the case without cancellation is achievedafter only one iteration at PER=0.01, and the system performance isrestored to within 1 dB of the non-clipped case after two iterations. Itis noted that the performance gain over the non-cancellation caseincreases as SNR increases. This is because at high SNR the AWGN noisebecomes relatively small and the clipping noise begins to dominate. Itis also noted that the performance of the signal reconstruction approachis worse by about 1.5 dB as compared with the methods and apparatus ofthe present invention.

FIG. 5 illustrates the simulated PER performance of the receiver 104over a Rayleigh fading channel with an exponentially decaying powerdelay profile, with normalized delay spread equal to 2. The channel isassumed to be constant over one packet and changes independently frompacket to packet. It can be seen that after one iteration theperformance of the clipped and filtered signals can be restored towithin 1 dB of the non-clipping case. This represents a gain of about 2dB at PER=0.01 as compared with the case without processing for themitigation of clipping effects. At PER=0.006, the gain becomes 2.8 dB.It is also noted that the performance of the signal reconstructionapproach performs worse by about 2 dB as compared with the presentinvention.

The simulation results show that the clipping noise cancellationapproach of the present invention can significantly restore theperformance. Further, more than about two iterations yields diminishingbenefit. The reason appears to be that there exist some OFDM symbolsthat are too badly damaged by clipping for the iterative process toconverge. This performance gap may be further narrowed by combining theapproach discussed above with bit or symbol interleaving methods. Sinceit is known at the transmitter 102 how the OFDM symbol is affected byclipping, the badly damaged symbols (according to some criterion) can beinterleaved and re-clipped, which may result in less clipping noise.

In the simulations for the fading channel, it was assumed that thechannel gain was perfectly known at the receiver 104. This is areasonable assumption since, with IEEE 802.11a, the PAPR of the trainingsymbols is designed to be only 3 dB and clipping is not required. Itfollows that clipping has no impact on channel estimation. Pilots may beinserted in the data symbols for phase tracking are distorted byclipping noise. In accordance with the present invention, however, theclipping noise is estimated and these pilots can be restored beforebeing processed.

With reference to FIG. 6, the clipping elements 110 and 140 may beimplemented using the repeated clipping approach. The details of thisclipping technique will not be discussed in great detail herein as theyare well known to those skilled in the art. Further details on therepeated clipping technique may be found, however, in J. Armstrong,“Peak-to-Average Power Reduction for OFDM by Repeated Clipping andFrequency Domain Filtering,” Electronics Letters, Vol. 38, pp. 246-247(February 2002), the entire disclosure of which is hereby incorporatedby reference.

The receiver 104 employing the repeated clipping technique has a similarstructure as in FIG. 1, except that clipping and filtering are repeatedto match the transmitter 102.

Using this technique, by repeating the digital clipping and filteringprocess with higher clipping ratio at each interval, the signals can beclipped to the same PAPR with less distortion. Without clipping noisecancellation, even with three or four times clipping and filtering thePAPR of the OFDM signal can be reduced only moderately (to 7 dB).Applying the repeated clipping approach to the transmitter 102 and thereceiver 104, it may be shown that the PAPR of the 64-subcarrier OFDMsignal can be reduced to 4 dB and the clipping noise cancellationapproach of the present invention restores the system performance towithin 1 dB of the non-clipping case.

This approach has also been the subject of simulation. In particular,the clipping and filtering at the transmitter 102 are repeated threetimes, with clipping ratios set to 1.5, 1.3 and 1.35 respectively. FIG.7 shows the PAPR distribution (CCDF) of the 64-subcarrier OFDM signalswith this set of clipping ratios. It is noted that the PAPR is reducedto 4 dB, an 8 dB reduction compared to the non-clipped case. Theclipping ratios used in the simulation has been chosen empirically.

FIG. 8 shows the PER performance of the system with repeated clipping.The channel model is the same Rayleigh fading channel as describedhereinabove. It is noted that the receiver 104 restores the systemperformance to within 1 dB of the non-clipped case after two iterations.This represents an improvement of about 2.5 dB at PER=0.01.

Advantageously, various aspects of the present invention permititerative distortion cancellation for clipped and filtered OFDM signals.The performance of a clipped and filtered OFDM system can besignificantly improved with only moderate complexity increase at thereceiver 104. In particular, the PAPR of the transmitted signal can besignificantly reduced with acceptable performance loss. The receiver 104is particularly suitable for IEEE 802.11a wireless LAN systems since itallows signals to be significantly clipped with only slight performancedegradation.

Although the invention herein has been described with reference toparticular embodiments, it is to be understood that these embodimentsare merely illustrative of the principles and applications of thepresent invention. It is therefore to be understood that numerousmodifications may be made to the illustrative embodiments and that otherarrangements may be devised without departing from the spirit and scopeof the present invention as defined by the appended claims.

1. A method, comprising: (a) transforming a received orthogonalfrequency division multiplexed (OFDM) signal from a transmission channelinto the frequency domain, using a device configured to transform asignal into the frequency domain, the OFDM signal having been subject toa clipping function prior to transmission; (b) recovering data symbolsfrom the transformed OFDM signal, the resulting data symbols includingclipping noise; (c) estimating the clipping noise in the frequencydomain based on attenuated versions of the data symbols; (d) subtractingthe estimated clipping noise from the transformed OFDM signal; and (e)outputting one or more recovered data symbols.
 2. An apparatus,comprising: a hardware frequency transform unit configured to transforma received orthogonal frequency division multiplexed (OFDM) signal tothe frequency domain, the received OFDM signal having been subject to aclipping function prior to transmission; a hardware decoding unitconfigured to recover data symbols from the frequency domain OFDMsignal, the resulting data symbols including clipping noise; a hardwareattenuator coupled to receive the data symbols as input and to outputattenuated data symbols; a hardware noise estimator configured toestimate the clipping noise in the frequency domain based on theattenuated data symbols; and a hardware difference circuit configured tosubtract the estimated clipping noise from the transformed OFDM signal.3. An apparatus including a non-transitory storage medium having storedthereon executable instructions and a processor coupled to the storagemedium, wherein the executable instructions, if executed by theprocessor, cause the apparatus to carry out actions comprising: (a)transforming a received orthogonal frequency division multiplexed (OFDM)signal from a transmission channel into the frequency domain, the OFDMsignal having been subject to a clipping function prior to transmission;(b) recovering data symbols from the transformed OFDM signal, theresulting data symbols including clipping noise; (c) estimating theclipping noise in the frequency domain based on attenuated versions ofthe data symbols; and (d) subtracting the estimated clipping noise fromthe transformed OFDM signal.
 4. A non-transitory storage medium havingstored thereon executable instructions, which if executed by a computingdevice, cause the computing device to carry out actions comprising: (a)transforming a received orthogonal frequency division multiplexed (OFDM)signal from a transmission channel into the frequency domain, the OFDMsignal having been subject to a clipping function prior to transmission;(b) recovering data symbols from the transformed OFDM signal, theresulting data symbols including clipping noise; (c) estimating theclipping noise in the frequency domain based on attenuated versions ofthe data symbols; and (d) subtracting the estimated clipping noise fromthe transformed OFDM signal.
 5. A method of reducing clipping noise,comprising: removing attenuated data symbols from clipped data symbolsto estimate clipping noise in the frequency domain in a deviceconfigured to estimate clipping noise; removing the estimated clippingnoise from a transformed orthogonal frequency division multiplexed(OFDM) signal; and outputting one or more recovered data symbols.
 6. Anarticle comprising: a non-transitory storage medium having storedthereon executable instructions, which if executed by a computingdevice, cause the computing device to perform operations in reducingclipping noise comprising: removing attenuated data symbols from clippeddata symbols to estimate clipping noise in the frequency domain; andremoving the estimated clipping noise from a transformed orthogonalfrequency division multiplexed (OFDM) signal.
 7. An apparatus,comprising: a computing platform; and a non-transitory storage mediumconfigured to be coupled to the computing platform and having storedthereon executable instructions, which if executed by the computingplatform, cause the apparatus to perform operations in reducing clippingnoise, the operations comprising: removing attenuated data symbols fromclipped data symbols to estimate clipping noise in the frequency domain;and removing the estimated clipping noise from a transformed orthogonalfrequency division multiplexed (OFDM) signal.
 8. The method according toclaim 1, wherein said estimating comprises: subtracting the attenuateddata symbols from clipped data symbols.
 9. The method according to claim1, further comprising repeating (a)-(d) at least twice to iterativelycancel clipping noise.
 10. The method according to claim 1, furthercomprising: applying channel gains to the estimated clipping noise priorto said subtracting.
 11. The apparatus according to claim 2, whereinsaid noise estimator comprises: a hardware differencing circuit toobtain a difference between said attenuated data symbols and an estimateof the clipped data symbols.
 12. The apparatus according to claim 2,further comprising: a hardware processing circuit to apply channel gainsto the estimated clipping noise prior to applying the estimated clippingnoise to said difference circuit.
 13. The apparatus according to claim3, wherein said estimating comprises: subtracting the attenuated datasymbols from clipped data symbols.
 14. The apparatus according to claim3, said actions further comprising repeating (a)-(d) at least twice toiteratively cancel clipping noise.
 15. The apparatus according to claim3, said actions further comprising: applying channel gains to theestimated clipping noise prior to said subtracting.
 16. The storagemedium according to claim 4, wherein said estimating comprises:subtracting the attenuated data symbols from clipped data symbols. 17.The storage medium according to claim 4, said actions further comprisingrepeating (a)-(d) at least twice to iteratively cancel clipping noise.18. The storage medium according to claim 4, said actions furthercomprising: applying channel gains to the estimated clipping noise priorto said subtracting.
 19. The method according to claim 5, wherein saidattenuated data symbols and said clipped data symbols are obtained froma received OFDM signal that was subject to clipping prior totransmission.
 20. The method according to claim 5, further comprising:performing said removing attenuated data symbols and said removing theestimated clipping noise at least twice to iteratively reduce clippingnoise.
 21. The method according to claim 5, further comprising:processing the estimated clipping noise using channel gains prior tosaid removing the estimated clipping noise.
 22. The article according toclaim 6, wherein the operations further comprise: performing saidremoving attenuated data symbols and said removing the estimatedclipping noise at least twice to iteratively reduce clipping noise. 23.The article according to claim 6, wherein the operations furthercomprise: processing the estimated clipping noise using channel gainsprior to said removing the estimated clipping noise.
 24. The apparatusaccording to claim 7, wherein said operations further comprise:performing said removing attenuated data symbols and said removing theestimated clipping noise at least twice to iteratively reduce clippingnoise.
 25. The apparatus according to claim 7, wherein said operationsfurther comprise: processing the estimated clipping noise using channelgains prior to said removing the estimated clipping noise.
 26. Anapparatus, comprising: means for transforming a received orthogonalfrequency division multiplexed (OFDM) signal from a transmission channelinto the frequency domain, wherein a clipping function was applied tothe OFDM signal prior to transmission; means for recovering data symbolsfrom the frequency domain OFDM signal; means for attenuating the datasymbols; means for estimating clipping noise in the frequency domainbased on the attenuated data symbols; and means for subtracting theestimated clipping noise from the transformed OFDM signal.
 27. Anapparatus for reducing clipping noise, comprising: means for removingattenuated data symbols from clipped data symbols to estimate clippingnoise in the frequency domain; means for removing the estimated clippingnoise from a transformed orthogonal frequency division multiplexed(OFDM) signal; and means for outputting one or more recovered datasymbols.